Terribly means very badly — he sings terribly, it went terribly wrong. But it is used far more often as a plain intensifier meaning very: terribly sorry, terribly kind of you, terribly clever.
That second use is British, common, and slightly posh in flavour — terribly is one of a small set of words including frightfully and awfully that lost all their fear and became emphasis. Note that the intensifier goes with both good and bad adjectives, so terribly pleased is not a contradiction, while terribly is the adverb of terrible and still means badly when it stands alone with a verb.
1adverbterriblyVery badly.
“The first attempt went terribly.”
2adverbextremelyVery — used as an intensifier.
“I am terribly sorry to have kept you.”
synonyms: very, extremely, awfully
terribly is a degree adverb.
Proto-Indo-European
*tres-
Middle English
terribli
English, today
terribly
Middle English terribli. by surface analysis, terrible + -ly.
Etymology from Wiktionary, CC BY-SA